Linux – Multiple network cards, controlling where the traffic goes

Why are you making life so difficult for yourself? You don't need a second NIC for that. Just add another IP address to the first NIC, so that it picks up the traffic for the other IP address, too.
Then do a port forwarding in your firewall, using DNAT, for both addresses, and to separate internal IP addresses (because of the SSL certificate) on the web server (which also needs to use two IP addresses in the same ethernet interface), and Bob's your uncle.

In case this isn't clear, let me try and explain differently:

Public IP
72.94.30.30 -> DNAT to 10.0.0.10 (ports 80 and 443)
72.94.30.31 -> DNAT to 10.0.0.11 (ports 80 and 443)
Both the public IP addresses use the same physical interface on the firewall/router and both the internal addresses use the same physical interface on the web server.

Based on that I'd suggest that your default route out of eth0 is taking precedence. Routing only cares about the best way to send a given packet, it doesn't care about general data flow. A client will attempt to connect to your server on xx.yy.zz.1 via eth0, but the response will be routed out of eth1 on 10.10.53.1. Even if the reply packet successfully reaches it's destination it will have the wrong IP address as a source and the client won't know what to do with it. You'll be able to verify if that's the case just by running packet captures on your interfaces as you make requests to the server.

Check out this guide on how to route packets back out of the interface they arrived on